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IEEE photonics journal

Tunable Goos–Hänchen Shift and Polarization Beam Splitting Through a Cavity Containing Double Ladder Energy Level System

Peng Han, Xiaoyang Chang, Wenxiu Li, Hao Zhang, Anping Huang, Zhisong Xiao

Published Feb 21, 2019• 6 citations
Publisher

Abstract

The present paper theoretically demonstrates tunable Goos-Hänchen (GH) shift and beam splitting of the polarized light reflected from the cavity containing the double ladder energy level system. Simultaneously opposite GH shifts for left-circularly polarized (LCP) and right-circularly polarized (RCP) beams can be achieved under asymmetric field conditions. By adjusting the intensity (Rabi frequency) of probe or drive field, the GH shifts of LCP and RCP probe beams are manipulated at the same time. We also discuss the effects of probe field frequency detuning on GH shifts and identify the parameters region to obtain a large separate distance (~320 μm) between LCP and RCP probe beams.

DOI
10.1109/jphot.2019.2897280

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Scientific Reports•Apr 17, 2025•0 citations
The present paper theoretically demonstrates tunable Goos-Hänchen (GH) shift and beam splitting of the polarized light reflected from the cavity containing the double ladder energy level system. Simultaneously opposite GH shifts for left-circularly polarized (LCP) and right-circularly polarized (RCP) beams can be achieved under asymmetric field conditions. By adjusting the intensity (Rabi frequency) of probe or drive field, the GH shifts of LCP and RCP probe beams are manipulated at the same time. We also discuss the effects of probe field frequency detuning on GH shifts and identify the parameters region to obtain a large separate distance (~320 μm) between LCP and RCP probe beams.
Abstract In this paper, we discuss Goos–Hänchen (GH) shifts of both reflected and transmitted light beams through a cavity containing single-layer graphene nanostructures. The Landau levels of a single layer graphene medium under a strong magnetic field can interact with infrared and terahertz signal radiation. Therefore, the GH shifts in both reflected and transmitted light beams can be obtained in the infrared and terahertz regions of radiation. We have realized that by controlling some adjustable parameters of the system, such as frequency detuning of applied fields, the Rabi frequency of a coupling field and the polarization of coupling light, the GH shifts can be manipulated in the infrared and terahertz regions. Moreover, the thickness of the intracavity medium is also considered as an important parameter on the behavior of GH shifts spectra.
The Goos and Hänchen (GH) shifts in reflected and transmitted probe light through a cavity mixture of left- and right-handed chiral molecules into two enantiomer states are investigated. Due to the broken mirror symmetry of the left- and right-handed chiral molecules in the presence of cyclic population transfer, such quantum systems can be selectively excited because of the coexistence of one- and two-photon transitions. With the help of coupling Rabi frequency and damping effects due to scattering processes, the generated GH shifts accompanied by simultaneously negative and positive lateral shifts in reflected and transmitted probe lights are greatly enhanced. It is found that the large negative and positive GH shifts are available in the presence of multiphoton resonance and off-resonance conditions for two different enantiomers' chiral molecules. Moreover, the switching between superluminal and subluminal light propagation is extremely dependent on choosing the left- and right-handed chiral molecules. Furthermore, the effects of pulse shape and mode of Laguerre-Gaussian probe light on the GH shifts that lead to a switch between negative and positive shift are also studied. The negative and positive GH shifts in a reflected and transmitted probe beam for an incident Gaussian and different mode of Laguerre-Gaussian shaped beam with various widths by the use of two different enantiomers' chiral molecules are also discussed.
The role of a chiral quantum-dot molecule (QDM) system in controlling and enhancing the Goos-H\"anchen (GH) shift is revealed here. The proposed setup is a four-level atomic system excited by incoherent pump and probe fields where the electron tunneling is prominent in affecting the GH shift upon the reflection and transmission of probe beams. The GH shifts in the chiral QDM system are calculated analytically by using stationary phase theory, whereas the dynamics of the quantum-dot system are derived by the density-matrix method. It is demonstrated that the GH shifts through transmission and reflection light beams are strongly influenced due to right-circularly polarized (RCP) and left-circularly polarized light. The GH shifts through RCP light are enhanced in the presence of chiral QDM systems, and these shifts could become either highly negative or highly positive, sensitively depending on the electron tunneling and chiral coefficients. This proposal can be viewed as a theoretical approach to the potential application of GH shifts in nano-optoelectronic sensors.
We have theoretically studied the Goos-Hänchen (GH) shifts of both the reflected and transmitted probe beams emerging from a cavity consisting of a hybrid system of a coupled quantum dot (QD) nanostructure and a metallic nanoparticle (MNP). It is realized that the GH shifts in the transmitted and reflected light beams can be enhanced due to the surface plasmon effect in the MNP. Also, it is shown that by adjusting the distance between QD and MNP and polarization control between probe field and major axis of the hybrid system, the simultaneous negative and positive GH shifts in reflected and transmitted light beams can occur. Moreover, the effects of the intensity and detuning of the coupling light on the GH shift properties of the reflected and transmitted lights have been discussed. We have found that under different parametric conditions of the hybrid system, the GH shifts of the reflected and transmitted light beams can be adjusted by tuning the intensity and controlling the detuning of the coupling field. The results show that our proposed model may be used for future optical sensor devices based on MNP hybrid systems.
The birefringence of reflection and transmission as well as their corresponding Goos–Hänchen shifts are investigated with complex conductivity in a four level chiral atomic medium. The left circularly polarized (LCP) beam and right circularly polarized (RCP) beam obey the normalization condition ∣R(R,L)∣+∣T(R,L)∣=1|R^{(R,L)}|+|T^{(R,L)}|=1∣R(R,L)∣+∣T(R,L)∣=1 with forward and backward currents as well as coupled driving fields parameters at the interface of a lossy chiral medium of ∣A(R,L)∣≃0|A^{(R,L)}|\simeq 0∣A(R,L)∣≃0 and polystyrene. For the birefringent transmission, the positive GH-shifts are reported while for the birefringent reflection, the negative GH-shifts are measured. The maximum GH-shift in reflections of RCP and LCP beams is measured to Sr(R,L)=−10λS^{(R,L)}_{r}=-10\lambdaSr(R,L)​=−10λ and that in the transmission is measured to St(R,L)=10λS^{(R,L)}_{t}=10\lambdaSt(R,L)​=10λ with forward and backward currents of complex conductivity. Furthermore, maximum values of GH-shifts in reflection and transmission of LCP beams are calculated to ±40λ\pm 40\lambda±40λ and RCP beams are calculated to ±10λ\pm 10\lambda±10λ with control field Rabi frequency and backward current variation. The results indicate possible uses in the designing of optical and conductive sensors.